Course Description: This course provides a working
knowledge of precalculus and its applications.
It begins with a review of algebraic operations . Emphasis is on solving and
graphing equations that involve
linear, polynomial, exponential, and logarithmic functions . Students learn to
graph trigonometric and inverse
trigonometric functions and learn to use the family of trigonometric identities.
Other topics include conic
sections, arithmetic and geometric sequences, and systems of equations.
Course Objectives: After completing this course, students will be able
to:
• Perform operations on real numbers and polynomials.
• Simplify algebraic, rational, and radical expressions .
• Solve linear and quadratic equations and inequalities.
• Solve word problems involving linear and quadratic equations and inequalities.
• Solve polynomial, rational, and radical equations and applications.
• Solve and graph linear, quadratic, absolute value, and piecewise-defined
functions.
• Perform operations with functions as well as find composition and inverse
functions.
• Graph quadratic, the square root , cubic, and cube root functions.
• Graph and find zeroes of polynomial functions.
• Graph quadratic functions by completing the square, using the vertex formula ,
and using
transformations.
• Solve and graph exponential and logarithmic equations.
• Express angle measure in degrees or radians.
• Evaluate and simplify trigonometric expressions.
• Know the six trigonometric functions and how to evaluate those trigonometric
functions using
positions on the unit circle with respect to the right triangle.
• Graph trigonometric and inverse trigonometric functions.
• Use trigonometric functions to solve a right triangle and apply the Law of
Sines and the Law of
Cosines to solve triangles that are acute or obtuse.
• Solve systems of linear equations and inequalities.
• Model and solve applications using linear systems.
• Evaluate and find partial sums of a series .
• Evaluate and find sums of an arithmetic sequence and a geometric sequence.
• Solve application problems involving arithmetic and geometric sequences and
series.
• Define, identify, and graph conic sections including circle, ellipse,
parabola, and hyperbola.
Course Text
Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th
edition, McGraw-Hill, 2008.
ISBN: 978-0-07-331263-7.
Important Terms
In this course, different terms are used to de signate tasks :
• Practice Exercise: A non-graded assignment to assist you in practicing the
skills discussed in a
topic.
• Graded Exam: A graded online test.
Course Evaluation Criteria
Students earn a percentage score. A passing percentage is 70% or higher.
There are a total of 500 points
in the course:
|
Topics |
Assessment |
Points Available |
|
1, 2, 3 & 4 |
Graded Exam #1 |
100 |
|
5, 6, 7 & 8 |
Graded Exam #2 |
100 |
|
9 & 10 |
Graded Exam #3 |
100 |
|
11, 12, 13 & 14 |
Graded Exam #4 |
100 |
|
Comprehensive Final |
Graded Exam #5 |
100 |
Yorktown University’s Official Grade Schedule:
Course Topics and Objectives
| Topic |
Lesson Topic |
Subtopics |
Objectives |
| 1
|
Basic Algebraic
Operations
|
• Real Numbers and
Polynomials
• Rational Expressions
• Rational Exponents and
Radicals
|
• Identify and use properties of real
numbers.
• Simplify algebraic expressions.
• Identify and classify polynomial
expressions.
• Perform operations on polynomials.
• Factor polynomials .
• Write a rational expression in simplest
form.
• Compute rational expressions.
• Simplify radical expressions.
• Multiply and divide radical expressions. |
| 2
|
Linear Equations and Inequalities in One
Variable
|
• Linear Equations and
Applications
• Linear Inequalities and
Applications
• Absolute Value in
Equations and
Inequalities |
• Solve linear equations by using all
properties of equality and the rules.
• Solve word problems using linear
equations.
• Use the notation of inequalities.
• Solve and graph linear inequalities.
• Solve an application using inequalities.
• Solve absolute value equations and
inequalities. |
| 3
|
Polynomial and
Other Equations
|
• Solving Polynomial
Equations
• Equations Involving
Radicals and Rational
Exponents
• Complex Numbers
|
• Solve quadratic equations using the
quadratic formula.
• Solve word problems involving quadratic
equations.
• Solve polynomial equations using the
zero factor property.
• Solve applications using these equation
types.
• Identify and simplify complex numbers.
• Add and subtract complex numbers.
• Multiply and divide complex numbers.
• Solve rational and radical equations.
• Solve quadratic equations using
factoring, the square root property, and
completing the square. |
| 4
|
Functions and Graphs
|
• Rectangular
Coordinates and the
Graph of a Line
• Relations, Functions,
and Graphs
• Linear Functions
|
• Use a table of values to graph linear
equations.
• Determine when lines are parallel or
perpendicular.
• Use linear graphs in an applied context.
• Identify functions and state their domain
and range.
• Use function notation.
• Write a linear equation in function form.
• Use function form to identify the slope .
• Use slope-intercept form to graph linear
functions.
• Write a linear equation in point-intercept
form.
• Use these forms to solve applications. |
| 5
|
Operations on
Functions and
Analyzing Graphs
|
• The Algebra and
Composition of
Functions
• One-to-One and Inverse
Functions
• Transformations and
Symmetry
|
• Compose two functions and find the
domain.
• Identify one-to-one functions.
• Find inverse functions using an algebraic
method .
• Graph a function and its inverse.
• Use symmetry as an aid to graphing.
• Perform stretches and compressions on
a basic graph.
• Perform vertical and horizontal shifts and
reflections of a basic graph. |
| 6
|
Graphing Polynomial
and Rational Functions
|
• Graphing Polynomial
Functions
• Asymptotes and
Rational Functions
• Graphing Rational
Functions
|
• Graph quadratic functions by completing
the square and using transformations.
• Graph a general quadratic function using
the vertex formula.
• Solve applications involving quadratic
functions.
• Graph polynomial functions.
• Identify horizontal and vertical
asymptotes.
• Use asymptotes to determine the
equation of a rational function from its
graph.
• Graph general rational functions.
• Solve applications involving rational
functions.
• Find the domain and intercepts of a
rational function. |
| 7
|
Exponential and Logarithmic Functions
|
• Exponential Functions
• Logarithms and
Logarithmic Functions
• The Exponential
Function and Natural
Logarithm
|
• Evaluate an exponential function.
• Graph exponential functions.
• Solve certain exponential equations.
• Write exponential equations in
logarithmic form.
• Graph logarithmic functions and find their
domains.
• Apply the properties of logarithms.
• Evaluate and graph the natural logarithm and exponential functions.
• Solve applications of logarithmic and
exponential functions. |
| 8
|
Exponential and Logarithmic Equations
|
• Exponential Equations
• Logarithmic Equations
• Applications of
Exponential and
Logarithmic Equations
|
• Write logarithmic and exponential
equations in simplified form.
• Solve exponential equations.
• Solve logarithmic equations.
• Solve applications involving exponential
and logarithmic equations.
• Use exponential equations to find the
interest compounded n times per year.
• Use exponential equations to find the
interest compounded continuously. |
| 9
|
An Introduction to Trigonometric
Functions
|
• Special Angles and the
Unit Circle
• Graphs of Basic
Trigonometric Functions
• Applications of Basic
Trigonometric Functions
|
• Correctly use vocabulary associated with
a study of angles and triangles.
• Convert between degrees and radians for nonstandard angles.
• Define the six trigonometric functions in
terms of a point on the unit circle or in
terms of a real number.
• Identify and discuss important
characteristics of tangent and cotangent.
• Solve applications of trigonometric
functions.
• Find values of the six trigonometric
functions from their ratio definition.
• Graph the basic trigonometric functions. |
| 10
|
Trigonometric Identities
|
• Transformations and
Applications of
Trigonometric Graphs
• Family of Trigonometric
Identities
• The Inverse
Trigonometric Functions
and Their Applications
|
• Use fundamental identities to express a
given trigonometric function in terms of
the other five.
• Solve applications using these identities.
• Find the inverse trigonometric functions
and evaluate related expressions.
• Apply the definition and notation of inverse trigonometric functions
to simplify
expressions.
• Graph sine and cosine functions with
various amplitudes and periods.
• Write the equation for a given graph. |
| 11
|
Applications of
Trigonometry
|
• The Law of Sines
• The Law of Cosines
• More Applications of
Trigonometry
|
• Solve ASA and AAS triangles.
• Use the Law of Sines to solve
applications.
• Apply the Law of Cosines when two sides
and an included angle are known (SAS).
• Apply the Law of Cosines when three
sides are known (SSS).
• Solve applications using the Law of
Cosines.
• Solve more applications involving trigonometric functions.
• Solve the SSA case, including the
ambiguous case. |
| 12
|
Systems of Linear
Equations in Two
Variables
|
• Solving Systems
Graphically, by
Substitution, and Using
Elimination
• Solving Linear Systems
Using Matrix Equations
• Applications of Linear Systems
|
• Solve linear systems by graphing, by
substitution, and by elimination.
• Use system of equations to
mathematically model and solve
applications.
• Form the augmented matrix of a system
of equations.
• Solve a system of equations using row operations.
• Recognize inconsistent and dependent systems.
• Use system of equations to
mathematically model and solve
applications. |
| 13
|
Conic Sections
|
• The Parabola
• The Ellipse and the
Circle
• The Hyperbola
|
• Define and identify a parabola.
• Graph a parabola.
• Solve applications of parabolas.
• Define and identify an ellipse and a
circle.
• Graph an ellipse and a circle.
• Solve applications of ellipses and circles.
• Define and identify a hyperbola.
• Graph a hyperbola.
• Solve applications of hyperbolas |
| 14
|
Sequences and Series
|
• Sequences and Series
• Arithmetic Sequences
• Geometric Sequences
|
• Write the terms of a sequence given the
general term.
• Determine the general term of a
sequence.
• Find the partial sum of a series.
• Use summation notation to write and
evaluate series.
• Solve applications involving arithmetic
sequences.
• Find the sum of a geometric series.
• Solve application problems involving
geometric sequences and series. |
| 15 |
Course Review |
• Course Review |
• None |
